Semisimple Algebras and a Cancellation Law.
Simple Flat Extensions. II.
Simple injective modules.
Small almost free modules with prescribed topological endomorphism rings
Some homological properties of amalgamated modules along an ideal
Let and be commutative rings with identity, be an ideal of , be a ring homomorphism, be an -module, be an -module, and let be an -homomorphism. The amalgamation of with along with respect to denoted by was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of -module called the amalgamation of and along with respect to , and denoted by . We study some homological properties of the -module . Among other results,...
Some morphisms of modules over the ring of pseudorational numbers.
Some remarks on Prüfer modules
We provide several characterizations and investigate properties of Prüfer modules. In fact, we study the connections of such modules with their endomorphism rings. We also prove that for any Prüfer module M, the forcing linearity number of M, fln(M), belongs to {0,1}.
Some Results about Modules over Discrete Hodge Algebras.
Some theorems on generation of ideals in affine algebras.
Stability, duality, 2-generated ideals and a canonical decomposition of modules
Stability Theorems for Overrings of Polynomial Rings.
Submodule of free Z-module
In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their proofs are...
Sur deux classes d'anneaux
Sur les algebres de Rees II.
Sylvester theorem for certain free modules